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Traditional theories of sensorimotor learning posit that animals use sensoryerror signals to find the optimal motor command in the face of Gaussian sensoryand motor noise. However, most such theories cannot explain common behavioralobservations, for example that smaller sensory errors are more readilycorrected than larger errors and that large abrupt (but not graduallyintroduced) errors lead to weak learning. Here we propose a new theory ofsensorimotor learning that explains these observations. The theory posits thatthe animal learns an entire probability distribution of motor commands ratherthan trying to arrive at a single optimal command, and that learning arises viaBayesian inference when new sensory information becomes available. We test thistheory using data from a songbird, the Bengalese finch, that is adapting thepitch (fundamental frequency) of its song following perturbations of auditoryfeedback using miniature headphones. We observe the distribution of the sungpitches to have long, non-Gaussian tails, which, within our theory, explainsthe observed dynamics of learning. Further, the theory makes surprisingpredictions about the dynamics of the shape of the pitch distribution, which weconfirm experimentally.

Chance, long tails, and inference: a non-Gaussian, Bayesian theory of vocal learning in songbirds